{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 100\n",
    "n = 5\n",
    "x = np.linspace(0, np.pi, N)\n",
    "xp = np.linspace(0, np.pi, n)\n",
    "y = np.sin(x)\n",
    "yp = np.sin(xp)\n",
    "z = np.zeros(N)\n",
    "zp = np.zeros(n)\n",
    "o = np.ones(N)\n",
    "op = np.ones(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fedfca18d90>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'r--')\n",
    "plt.plot(xp, yp, 'o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lag(xp, x, i):\n",
    "    r1 = np.prod(np.array(x) - [*xp[0:i], *xp[i + 1:]])\n",
    "    r2 = np.prod(xp[i] - [*xp[0:i], *xp[i + 1:]])\n",
    "    return r1 / r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = len(x)\n",
    "l0 = np.zeros(N)\n",
    "for i in range(0, N):\n",
    "    l0[i] = lag(xp, x[i], 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fedfc8beca0>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'r--')\n",
    "plt.plot(xp, yp, 'ro')\n",
    "plt.plot(x, z, 'b--')\n",
    "plt.plot(xp, zp, 'bo')\n",
    "plt.plot(x, o, 'k--')\n",
    "plt.plot(xp, op, 'ko')\n",
    "plt.plot(x, l0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "l1 = np.zeros(N)\n",
    "for i in range(0, N):\n",
    "    l1[i] = lag(xp, x[i], 1)\n",
    "l2 = np.zeros(N)\n",
    "for i in range(0, N):\n",
    "    l2[i] = lag(xp, x[i], 2)\n",
    "l3 = np.zeros(N)\n",
    "for i in range(0, N):\n",
    "    l3[i] = lag(xp, x[i], 3)\n",
    "l4 = np.zeros(N)\n",
    "for i in range(0, N):\n",
    "    l4[i] = lag(xp, x[i], 4)   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fedfc859b50>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, 'r--')\n",
    "plt.plot(xp, yp, 'ro')\n",
    "plt.plot(x, z, 'b--')\n",
    "plt.plot(xp, zp, 'bo')\n",
    "plt.plot(x, o, 'k--')\n",
    "plt.plot(xp, op, 'ko')\n",
    "plt.plot(x, l0)\n",
    "plt.plot(x, l1)\n",
    "plt.plot(x, l2)\n",
    "plt.plot(x, l3)\n",
    "plt.plot(x, l4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Runge(x):\n",
    "    return 1.0 / (1.0 + x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10\n",
    "xp = np.linspace(-5, 5, n)\n",
    "yp = Runge(xp)\n",
    "l = np.zeros((n, N))\n",
    "x = np.linspace(-5, 5, N)\n",
    "for i in range(0, n):\n",
    "    for j in range(0, N):\n",
    "        l[i][j] = lag(xp, x[j], i)\n",
    "y = np.zeros(N)\n",
    "for j in range(0, N):\n",
    "    for i in range(0, n):\n",
    "        y[j] = y[j] +  l[i][j] * yp[i] \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fedfc7e3940>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, Runge(x), '--')\n",
    "plt.plot(x, y, 'b')\n",
    "plt.plot(xp, yp, 'ro')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fedfc6faa00>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 10\n",
    "xp = np.linspace(-1, 1, n)\n",
    "l = np.zeros((n, N))\n",
    "x = np.linspace(-1, 1, N)\n",
    "for i in range(0, n):\n",
    "    for j in range(0, N):\n",
    "        l[i][j] = lag(xp, x[j], i)\n",
    "zp = np.zeros(n)\n",
    "op = np.ones(n)\n",
    "for i in range(n):\n",
    "    plt.plot(x, l[i])\n",
    "plt.plot(xp, zp, 'bo')\n",
    "plt.plot(xp, op, 'bo')\n",
    "T = np.cos(n * np.arccos(x))\n",
    "plt.plot(x, T, 'k--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fedfc6af430>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(n):\n",
    "    xp[i] = np.cos((2 * i + 1) / (2 * n) * np.pi)\n",
    "for i in range(0, n):\n",
    "    for j in range(0, N):\n",
    "        l[i][j] = lag(xp, x[j], i)\n",
    "for i in range(n):\n",
    "    plt.plot(x, l[i])\n",
    "plt.plot(xp, zp, 'bo')\n",
    "plt.plot(xp, op, 'bo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "yp = Runge(xp)\n",
    "y = np.zeros(N)\n",
    "for j in range(0, N):\n",
    "    for i in range(0, n):\n",
    "        y[j] = y[j] +  l[i][j] * yp[i]   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fedd82d3dc0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, Runge(x), '--')\n",
    "plt.plot(x, y, 'b')\n",
    "plt.plot(xp, yp, 'ro')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.98768834,  0.89100652,  0.70710678,  0.4539905 ,  0.15643447,\n",
       "       -0.15643447, -0.4539905 , -0.70710678, -0.89100652, -0.98768834])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
